Many well tools operated in response to a hydraulic signal also have provisions for mechanical operation, for example with a shifting tool of a work string or a wire run actuator tool. Such provisions enable contingent mechanical operation of the well tool when the hydraulic operation is impossible or impracticable. For example, a deep set Surface Controlled Subsurface Safety Valve (SCSSV) can sometimes become inoperable due to well debris and can stick in an open, closed or partially closed position when operated during periodic downhole testing. Because of the small operating piston area of the hydraulic actuator and the limited forces produced by the valve's return spring, it is sometimes not possible to fully operate the SCSSV with the available control line pressure. Wire run and operated exercise tools exist, for example, the Safety Valve Exercise Tool “42TLXXX” made and sold by Halliburton Energy Services, Inc. Such an exercise tool is locked into a profile in the SCSSV flow tube and upward and downward jarring along with control line pressure is used to force movement of the actuator sleeve in the SCSSV. This jarring action is sometimes ineffective because the exercise tool must work against the SCSSV spring, hydraulic piston and the lubricator seal.